Field of Invention
This invention relates to educational devices, specifically to such devices that are used for observing place-value names, notation, and properties of whole numbers and decimal numbers. Impetus: Introduces invention in more complete terms of what is presented and was previously presented in initial application.
Prior Art
Various aids and devices have long been used to assist students in their understanding of mathematic concepts. In using these devices, teachers ideally engage various student learning modalities. The recognized modalities are informally defined as seeing, touching, hearing, and moving. In the introductory stages of numeracy, the modality of seeing, or observation, is regularly and successfully used.
As instruction progresses to operations beyond single digits, place-value names, such as Ones and Tens, and place-value properties must be explored. Accordingly, many devices have been introduced to help explain place-value concepts. Until now, these devices have largely minimalized the modality of observation and instead rely heavily on teacher explanation, or the hearing modality. The effectiveness of teacher explanation, as well as teacher confidence with the use of such devices, often varies widely between classrooms. As a result, the student's foundational, place-value understanding and general interest in mathematics may be placed at risk, delayed, or severely compromised. The effects of these problems and weaknesses are perpetuated when new place-value properties are revisited in the study of decimal place value.
Along with the disadvantages of the prior art devices regarding learning modalities, other weaknesses are notable. Many of these devices rely on cognitive input or numeric manipulation of individual digits or individual place names. Each are therefore capable of generating incorrect answers or of reinforcing misconceptions. U.S. Pat. No. 2,804,699 to Robinson (1957) uses numbered and named tiles with which to display various numeric values and place names. This device uses a moveable decimal point, and the names and values of various places may be randomly chosen. As such, this device requires continual teacher oversight and instruction to correct faulty manipulations and subsequent misconceptions.
Because the relevant, prior art place-value devices rely on teacher explanation and skill, they are subjective in nature. As such, they do not assure a consistent, accurate display of decimal and whole-number place-value concepts. U.S. Pat. No. 6,729,883 to Raiche (2004) teaches the use of a device with numbered wheels with which to display numeric values. This device uses a non-moveable decimal point to accommodate the display of both decimal and whole-number place values. However, the place values may be randomly chosen, and the wheels may be independently rotated in segmented or non-sequential fashion. It may thus lend itself to inefficient or inconsistent presentations of concepts.
Several other numeric educational devices use sequential numbers printed on rotatable surfaces. U.S. Pat. No. 2,476,580 to Bergman (1949) teaches the use of a device having numbered wheels, an answer disk, and interchangeable operations symbols. This device uses a sequential display of one and two-digit whole numbers to solve single-digit addition and subtraction problems. Its effective range of correct answers, without disassembly of the device, is 0-18. Its total stated range of sequential number display is 0-59. This device cannot display an unbroken numeric sequence of 0-99. Its place values are limited in scope to a narrow range of sequences in the Ones and Tens places only. It accommodates neither the display of decimal place values, nor the observation of decimal place value properties.
Thus, in the field of place-value teaching devices, nowhere in the prior art is found a device which can assure an accurate presentation of the sequential, dynamic nature of whole-number and decimal place value names, notation, and properties in a consistent, objective fashion that is independent of the variables of user skill and resistant to user error.